Effect of Short Implant Crown-To-Implant Ratio On
Effect of Short Implant Crown-To-Implant Ratio On
Effect of Short Implant Crown-To-Implant Ratio On
Abstract
Objective This study aimed to provide evidence for the clinical application of single short implants by establishing
an anisotropic, three-dimensional (3D) finite element mandible model and simulating the effect of crown-to-implant
ratio (CIR) on biomechanics around short implants with different osseointegration rates.
Methods Assuming that the bone is transversely isotropic by finite element method, we created four distinct models
of implants for the mandibular first molar. Subsequently, axial and oblique forces were applied to the occlusal surface
of these models. Ultimately, the Abaqus 2020 software was employed to compute various mechanical parameters,
including the maximum von Mises stress, tensile stress, compressive stress, shear stress, displacement, and strains
in the peri-implant bone tissue.
Results Upon establishing consistent osseointegration rates, the distribution of stress exhibited similarities
across models with varying CIRs when subjected to vertical loads. However, when exposed to inclined loads, the max-
imum von Mises stress within the cortical bone escalated as the CIR heightened. Among both loading scenarios,
notable escalation in the maximum von Mises stress occurred in the model featuring a CIR of 2.5 and an osseointegra-
tion rate of 25%. Conversely, other models displayed comparable strength. Notably, stress and strain values uniformly
increased with augmented osseointegration across all models. Furthermore, an increase in osseointegration rate
correlated with reduced maximum displacement for both cortical bone and implants.
Conclusions After fixing osseointegration rates, the stress around shorter implants increased as the CIR increased
under inclined loads. Thus, the effect of lateral forces should be considered when selecting shorter implants. Moreo-
ver, an implant failure risk was present in cases with a CIR ≥ 2.5 and low osseointegration rates. Additionally, the higher
the osseointegration rate, the more readily the implant can achieve robust stability.
Keywords Short implant, Osseointegration rate, Crown-to-implant ratio, Three-dimensional finite element
*Correspondence:
Yang Liu
liuyang913015@163.com
Full list of author information is available at the end of the article
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characteristics, boundary and load conditions, cell type, of the crown-to-implant ratio on bone stress distribu-
grid sensitivity, and contact definition [20]. tion around short implants, considering varying bone
Previous FEM studies have analyzed the properties of binding rates. This endeavor aims to provide insights
bones as osseointegrated and isotropic. A quantitative for designing short implants for diverse bone healing
clinical assessment showed an absence of complete osse- circumstances.
ointegration and suggested that bones exhibited different
mechanical properties when measured in different direc-
tions [21]. Thus, these findings confirmed that the peri- Materials and methods
implant osseointegration rate cannot reach 100%, and Experimental equipment
the bone is an anisotropic tissue. Different studies have We used the following hardware: Dell commercial desk-
utilized varied osseointegration rates, such as randomly top computer, 64 GB RAM, 128 GB hard drive, and Win7
connecting the bone-implant interface according to the 64-bit operating system, as well as a 3Shape R700 scanner
designated osseointegration rate and establishing uni- (3Shape, Copenhagen, Denmark).
form pore-like structural bone tissue [22, 23]. Although We used the following software: SolidWorks 2019 3D
these methods utilized the osseointegration rates, they computer-aided design software (SolidWorks Corp,
were unrealistic and did not consider the anisotropy USA), Geomagic studio2012 software (Geomagic, Inc),
characteristics of bones. Additionally, few studies only HyperMesh 12.0 (Altair, Inc), and Abaqus 2020 (Das-
considered the anisotropic characteristics and bone- sault, USA).
deficient osseointegration rates [24, 25]. Therefore, the
results obtained by the previous simplified method were
not accurate, thus, limiting its clinical application. Grouping
In our study, a transition region of the bones was defined We investigated the stress distribution around short
to represent partial osseointegration that stimulates the implants in four different CIRs under Class III bone con-
condition of peri-implant bones accurately. As the corti- ditions with varying osseointegration rates. The short
cal bone’s elastic modulus was similar to that of the can- implants used were: Straumann columnar soft tissue hor-
cellous bone in buccolingual and mesiodistal directions, izontal implants with a size of 4.8 × 6 mm. Furthermore,
we assumed that the bones were transversely isotropic the implants were divided into four model groups with
and longitudinally anisotropic [16]. Additionally, implant CIRs of 1, 1.5, 2, and 2.5, respectively.
restorations in atrophic jaws are challenging because the
atrophic jaws contain Class III bones with low bone mass
and poor quality [26]. We also used CIR as an independ- Establishment of models
ent factor to simulate stresses and strains in peri-implant Establishment of the local mandible model
bones caused by occlusal loading in Class III bones and to Solidworks 2019 three-dimensional (3D) software was
analyze the effects of osseointegration degree. used for establishing a dentition defect model in the pos-
However, there is a lack of biomechanical stud- terior mandibular region. The model’s measurements,
ies on the CIR of short implants under different osse- i.e., the jaw height, mesiodistal diameter, and buccolin-
ointegration rates in previous studies. Hence, the gual diameter at the alveolar crest, were established at
objective of this experiment was to assess the impact 23.1 mm, 20 mm, and 17 mm, respectively (Fig. 1).
Table 3 Maximum von Mises stress on the cortical bone Analysis of physicomechanical properties
Maximum von Mises stress
The maximum von Mises stress, tensile stress, compres-
(MGPa) sive stress, shear stress, maximum displacement, maximum
strain, and stress distribution map calculated for each group
Vertical load Inclined load
were analyzed. Although the yield strength of cortical bone
BIC = 25% 1:1 C/I 27.06 23.00 was 160 MPa, the yield strength of different osseointegra-
1.5:1 C/I 27.06 26.48 tion rates changed proportionally with the magnitude of the
2:1 C/I 27.05 31.71 osseointegration rate [16]. The ultimate tensile and com-
2.5:1 C/I 27.05 42.17 pressive strengths of the cortical bone were approximately
BIC = 50% 1:1 C/I 32.47 27.07 100–121 MPa and 167–173 MPa, respectively [31].
1.5:1 C/I 32.47 31.07
2:1 C/I 32.47 37.08 Results
2.5:1 C/I 32.47 49.11 Maximum von Mises stress and stress distribution
BIC = 75% 1:1 C/I 35.53 29.47 Figure 6 shows the changes in maximum von Mises
1.5:1 C/I 35.53 33.78 stress for all the models under vertical and inclined loads,
2:1 C/I 35.52 40.25 respectively. In both loading conditions, the models’ corti-
2.5:1 C/I 35.52 53.21 cal bone was subjected to the maximum von Mises stress
BIC = 100% 1:1 C/I 37.56 31.09 within its yield strength range, except for the model with a
1.5:1 C/I 37.55 35.61 CIR of 2.5 and an osseointegration rate of 25%, as shown
2:1 C/I 37.55 42.40 in Table 3. After fixing the osseointegration rates, similar
2.5:1 C/I 37.55 56.00 stress values were obtained from the models with different
CIRs under vertical loads. Moreover, after fixing the osse-
ointegration rate, the maximum von Mises stress on the
Table 4 Tensile stress, compressive stress, and shear stress on the cortical bone
Maximum tensile stress (MGPa) Maximum compressive stress Maximum shear stress (MGPa)
(MGPa)
Vertical load Inclined load Vertical load Inclined load Vertical load Inclined load
BIC = 25% 1:1 C/I 26.31 15.98 36.18 30.87 8.24 6.76
1.5:1 C/I 26.31 20.07 36.18 35.57 8.24 7.73
2:1 C/I 26.31 27.43 36.18 42.63 8.24 9.29
2.5:1 C/I 26.31 42.15 36.18 56.74 8.24 12.45
BIC = 50% 1:1 C/I 30.33 21.61 43.77 36.61 8.26 6.76
1.5:1 C/I 30.33 24.54 43.77 42.07 8.26 7.73
2:1 C/I 30.33 32.36 43.77 50.25 8.26 9.29
2.5:1 C/I 30.33 49.62 43.77 66.64 8.26 12.45
BIC = 75% 1:1 C/I 33.48 24.73 48.01 39.98 8.29 7.17
1.5:1 C/I 33.49 28.04 48.01 45.89 8.29 8.32
2:1 C/I 33.49 35.42 48.00 54.77 8.29 10.04
2.5:1 C/I 33.49 54.24 48.00 72.52 8.29 13.49
BIC = 100% 1:1 C/I 35.60 26.71 50.81 42.28 8.32 7.59
1.5:1 C/I 35.60 30.25 50.81 48.51 8.32 8.82
2:1 C/I 35.60 37.59 50.80 57.86 8.32 10.67
2.5:1 C/I 35.60 57.48 50.80 76.58 8.32 14.38
cortical bone under inclined loads increased as the CIR of tensile and compressive strengths in all the models.
escalated. Additionally, an increase in osseointegration Under the vertical loads, the three forces in the models
rate also enhanced the maximum von Mises stress by 30% with different CIRs did not show any significant differ-
within the same CIR. ence. However, under inclined loads, the tensile stress,
According to the stress distribution maps mentioned compressive stress, and shear stress on the cortical
below (Figs. 7 and 8), the stress was concentrated in the bone increased as the osseointegration rate increased,
implant neck region in all the models regardless of CIR or including a 37%-35%, 36–67%, and 16–23% increase
osseointegration rates. Furthermore, the stress distribu- in compressive stress, tensile stress, and shear stress,
tion in the cancellous bone region was uniform. respectively. Moreover, the tensile stress was more
susceptible to osseointegration rate than compres-
Tensile stress, compressive stress, and shear stress sive stress. Similarly, tensile stress, compressive stress,
As shown in Table 4, the cortical bone’s tensile and and shear stress all increased with the enhancement of
compressive stresses were within the required range CIRs (Fig. 9).
Fig. 9 Tensile stress, compressive stress, and shear stress on the cortical bone
Maximum strain occurred in the implant and the cancellous bone regions,
According to Fig. 10, the maximum strain of cortical respectively. Although the maximum displacement under
bone did not show any significant difference with differ- vertical loads was similar in magnitude, the maximum
ent CIRs under vertical loads but displayed significant displacement increased with enhanced CIR in inclined
differences under inclined loads. The maximum strain loads. However, the maximum displacement decreased
of the cortical bone under inclined loads increased with as the osseointegration rate increased at the same CIR
the enhancement of CIR. Moreover, at the same CIR, the (Table 6).
higher the osseointegration rate, the lesser the maximum
strain of the cortical bone (Table 5). Discussion
The usage of short implants in posterior regions with
Maximum displacement insufficient vertical bone height might provide advan-
Figures 11, 12, and 13 show the maximum displace- tages in terms of fewer treatment costs and sessions as
ment of the cortical and cancellous bones, as well as the well as a lower incidence of complications. However,
implant under vertical and inclined loads, respectively. In their application was often accompanied by a higher
all the models, the greatest and the smallest displacement CIR. Because of the leverage effect, higher CIRs induced
Table 5 Maximum strain of the cortical bone facilitate calculations. The stress values while calculating
Maximum strain
isotropy were 20%–30% higher than the values obtained
in transverse isotropy [36]. When the calculated stress
Vertical load Inclined load was lower than the bone’s yield strength, it indicated that
BIC = 25% 1:1 C/I 0.65 0.43 this value was within the loading range of the bone. Addi-
1.5:1 C/I 0.65 0.54 tionally, Kurniawan et al. [16] proposed a theory of dif-
2:1 C/I 0.65 0.73 ferent yield strengths at different osseointegration rates
2.5:1 C/I 0.65 1.12 and confirmed that the maximum von Mises stress on
BIC = 50% 1:1 C/I 0.4 0.29 the cortical bone around the short implant exceeded the
1.5:1 C/I 0.4 0.33 yield strength at an osseointegration rate of 25% and a
2:1 C/I 0.4 0.43 CIR of 2.5. Thus, these results suggested that the implant
2.5:1 C/I 0.4 0.66 failure risk was higher when the CIR was ≥ 2.5. Hence,
BIC = 75% 1:1 C/I 0.29 0.22 short implants should be carefully selected according to
1.5:1 C/I 0.29 0.25 the patient’s conditions and occlusal habits.
2:1 C/I 0.29 0.31 Although the stress distribution on the implant and
2.5:1 C/I 0.29 0.48 bones was uniform in vertical loading, the maximum
BIC = 100% 1:1 C/I 0.23 0.18 von Mises stress distribution pattern did not change
1.5:1 C/I 0.23 0.2 significantly with an enhanced CIR. This might have
2:1 C/I 0.23 0.25 occurred because the direction of force transmission
2.5:1 C/I 0.23 0.38 occurred on the implant’s long axis, resulting in a non-
significant increase in tension [37]. However, the maxi-
mum von Mises stresses on the implant and bones were
positively correlated with CIRs under inclined loads;
enhanced stresses in the implant and the surrounding this finding was consistent with the results obtained by
bones. Consequently, these stresses may cause marginal Ercal et al. [6]. Similarly, Sutpideler et al. [38] also dem-
bone resorption, screw loosening, and implant frac- onstrated that the stress increased as the crown height
ture and severely affect long-term restorative outcomes expanded under inclined loads. Furthermore, our results
[32]. A study showed that increased crown height was confirmed that the implants were significantly affected
a more significant factor than decreased implant length by inclined loads, thereby suggesting that lateral forces
in causing implant failure [33]. The short implants fre- should be duly considered in short implant restorations.
quently utilized in clinical settings are the 6 mm soft Moreover, the lateral masticatory forces can be curtailed
tissue level short implants from Straumann. Thus, this in patients by reducing their buccolingual diameter and
study employed the Straumann 6 mm short implant. It cusp inclination.
increased the crown height while maintaining a constant Additionally, we proposed that the maximum von
length to conduct a biomechanical analysis involving dis- Mises stresses on the cortical bone were higher as the
tinct models. CIR increased under non-axial loads. The longer the
Moreover, the implant’s CIR can be divided into clini- crown height of the fixed-length implants was, the
cal and anatomical CIRs. The clinical CIR is the ratio greater the lever force and the marginal bone loss. Hing-
between the distance from the apex to the implant- samer et al. [39] revealed that the short implants with a
bone interface and the distance from the implant-bone CIR of ≥ 1.7 were prone to marginal bone loss. Addition-
interface to the bottom of the implant. Additionally, the ally, Meijer et al. [15], in a meta-analysis of single-crown
anatomical CIR incorporates the prosthesis-abutment restorations supported by short implants, confirmed that
shoulder as the boundary rather than the implant-bone no significant differences were observed in retention rate
interface [34]. However, alveolar bone resorption reduced and marginal bone resorption when the single crown CIR
the clinical CIR, whereas anatomical CIR did not change. was 0.86–2.14. On the contrary, Garaicoa-Pazmiño et al.
Therefore, clinical CIR was more reflective of the clini- [12], in a systematic review, concluded that when the CIR
cal reality of implants [35]. We used clinical CIR, and the was 0.6–2.36, the greater the CIR, the lower the bone
stress distribution at different CIRs was simulated under resorption. They suggested a high CIR promoting bone
Class III bone conditions. remodeling activity might be preventing marginal bone
Although bone is considered an anisotropic material, resorption [40, 41]. Another study by Takahashi et al. [31]
its material behavior can further categorize the character- concluded that augmentation surgery was not required in
istics as transverse isotropic and longitudinal anisotropic. cases where the crown height was < 15 mm; the reduced
Hence, we assumed that bone was transverse isotropic to crown height helped in proper stress distribution in the
bone around short implants. However, the aforemen- the ideal biomechanical environment requires a balance
tioned literature did not consider the crown height, between tensile stress and compressive stress. Since
which might be one of the reasons for varying conclu- shear stress promotes slippage at the bone-implant
sions. Our results suggested that the short implants were interface, it is the least unfavorable force for implant
successful at higher osseointegration rates with a CIR of stability. Our results suggested that although both ten-
2.5. Therefore, short implants with high CIR can achieve sile and compressive stress increased with enhanced
higher success rates in controlled occlusal and parafunc- osseointegration rate, tensile stress was more easily
tional habits, thereby allowing the establishment of a rea- affected by the osseointegration rate. This may be due
sonable crown height. to the synergism between osseointegration and com-
In general, occlusal masticatory forces generate three pressive stresses. Furthermore, the magnitude of shear
different forces at the implant-bone interface; tensile stress increased as the CIR increased, indicating that
stress, compressive stress, and shear stress [21]. Com- the greater the CIR, the enhanced the likelihood of
pressive stress can enhance bone strength, while tensile implant slippage. Therefore, implant design factors,
stress can pull apart or stretch the material. Therefore, such as thread shape, should be considered to minimize
the shear stress when choosing shorter implants with tolerable for bones with higher osseointegration rates
large CIRs. as their stress values were lower relative to their yield
Our results showed that the maximum von Mises stress strengths. Additionally, the maximum displacement neg-
and strain on the cortical bone increased and decreased atively correlated with the osseointegration rate under
as the osseointegration rate increased at the same CIR. inclined loads.
These findings demonstrated that deformation was The maximum von Mises stress distribution patterns
required for bones with a low osseointegration rate to in our study showed that the maximum stress was con-
compensate for such loads. Additionally, the stress– centrated in the implant neck region in all models and
strain relationship was a form of energy (the area under was consistent with previous studies. In natural teeth,
the stress–strain curve equaled the strain energy), which the presence of periodontal ligament provides certain
suggested that osteocytes with lower osseointegration mobility, thereby avoiding the stress concentration on the
rates needed Simultaneously, Kurniawan et al. [16] pro- cortical bone. However, as osseointegrated implants are
posed that different osseointegration rates corresponded attached to the bone through surface micropores with a
to different yield strengths, and higher stresses were rigid interface, the external loads are directly transmitted
to the bone without buffering; therefore, stress is often notably displays orthogonal anisotropy and viscoelastic
concentrated around the implant neck area. behavior. Furthermore, the interplay between bone and
There were some limitations in our study. Although this implant changes over time. These variables collectively
3D FEA was a simulation study and the numerical model influence the experimental outcomes to a certain extent.
was appropriately simplified, the complex oral environ- This study is unable to entirely replicate real clinical sce-
ment cannot be reproduced distinctly. Biological sys- narios and can solely offer theoretical data to substan-
tems exhibit the capacity to adapt in response to external tiate biomechanical aspects. The utilization of CBCT
stimuli. Thus, when employing the finite element method data can facilitate the construction of precise models,
within the context of biological medicine, some dispari- enhancing the alignment of the model with clinical prac-
ties from actual situations may arise [18]. Additionally, tice [42]. Concurrently, we will pursue ongoing clinical
despite acknowledging the existence of transverse iso- investigations to validate these findings. Additionally,
tropic bone properties, bone is still represented as a lin- there is a lack of studies on stress distribution with crown
ear elastic continuum. It is noteworthy that the mandible heights > 15 mm, which should be further explored.
Table 6 Maximum displacement of the cortical bone, cancellous bone, and implant
Maximum displacement under vertical loads Maximum displacement under inclined loads
Cortical bone Cancellous bone Implant Cortical bone Cancellous bone Implant
BIC = 25% 1:1 C/I 0.0406 0.0405 0.0409 0.0321 0.0300 0.0405
1.5:1 C/I 0.0406 0.0405 0.0409 0.0354 0.0329 0.0454
2:1 C/I 0.0406 0.0405 0.0409 0.0403 0.0372 0.0530
2.5:1 C/I 0.0406 0.0405 0.0409 0.0502 0.0458 0.0680
BIC = 50% 1:1 C/I 0.0346 0.0346 0.0349 0.0294 0.0279 0.0368
1.5:1 C/I 0.0346 0.0346 0.0349 0.0323 0.0305 0.0412
2:1 C/I 0.0346 0.0346 0.0349 0.0367 0.0345 0.0478
2.5:1 C/I 0.0346 0.0346 0.0349 0.0456 0.0424 0.0610
BIC = 75% 1:1 C/I 0.0322 0.0321 0.0325 0.0282 0.0269 0.0353
1.5:1 C/I 0.0322 0.0321 0.0325 0.0310 0.0294 0.0394
2:1 C/I 0.0322 0.0321 0.0325 0.0352 0.0332 0.0456
2.5:1 C/I 0.0322 0.0321 0.0325 0.0437 0.0409 0.0581
BIC = 100% 1:1 C/I 0.0308 0.0307 0.0311 0.0276 0.0263 0.0344
1.5:1 C/I 0.0308 0.0307 0.0311 0.0303 0.0289 0.0384
2:1 C/I 0.0308 0.0307 0.0311 0.0344 0.0326 0.0444
2.5:1 C/I 0.0308 0.0307 0.0311 0.0426 0.0401 0.0565
Conclusion Declarations
Our study yielded the following conclusions:
Ethics approval and consent to participate
Not applicable.
(1) When the osseointegration rate is the same, there is
Consent for publication
no significant difference in the stress values among Not applicable.
various crown-to-implant ratios under vertical
loading. However, under oblique loading condi- Competing interests
The authors declare no competing interests.
tions, the crown-to-implant ratio demonstrates a
positive correlation with stress values. When opting Author details
for short implants, efforts should be made to mini- 1
Affiliated Hospital of Shaanxi University of Chinese Medicine, Xian-
yang 712000, China. 2 Dalian University of Technology, Dalian 116000, China.
mize lateral forces. 3
Dalian Stomatological Hospital, Dalian 116000, China. 4 Dalian University,
(2) When the crown-to-implant ratio reaches 2.5 or Dalian 116000, China. 5 Department of Prosthodontics, Dalian Stomatological
higher, it is imperative to thoroughly assess the Hospital, 935 Changjiang Road, Shahekou District, Dalian 116000, China.
patient’s individual circumstances and exercise cau- Received: 26 June 2023 Accepted: 31 August 2023
tion when contemplating the use of short implants.
Acknowledgements
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